{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introducing Keras\n",
    "\n",
    "Be sure to be using tensorflow 1.9 or newer!\n",
    "\n",
    "Keras is a higher-level API within TensorFlow that makes things a lot easier. Not only is it easier to use, it's easier to tune.\n",
    "\n",
    "Let's set up the same deep neural network we set up with TensorFlow to learn from the MNIST data set.\n",
    "\n",
    "First we'll import all the stuff we need, which will initialize Keras as a side effect:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow import keras\n",
    "from tensorflow.keras.datasets import mnist\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense, Dropout\n",
    "from tensorflow.keras.optimizers import RMSprop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll load up the MNIST data set. In Keras, it's a little bit different - there are 60K training samples and 10K test samples. No \"validation\" samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(mnist_train_images, mnist_train_labels), (mnist_test_images, mnist_test_labels) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to explicitly convert the data into the format Keras / TensorFlow expects. We divide the image data by 255 in order to normalize it into 0-1 range, after converting it into floating point values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_images = mnist_train_images.reshape(60000, 784)\n",
    "test_images = mnist_test_images.reshape(10000, 784)\n",
    "train_images = train_images.astype('float32')\n",
    "test_images = test_images.astype('float32')\n",
    "train_images /= 255\n",
    "test_images /= 255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll convert the 0-9 labels into \"one-hot\" format, as we did for TensorFlow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_labels = keras.utils.to_categorical(mnist_train_labels, 10)\n",
    "test_labels = keras.utils.to_categorical(mnist_test_labels, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a peek at one of the training images just to make sure it looks OK:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def display_sample(num):\n",
    "    #Print the one-hot array of this sample's label \n",
    "    print(train_labels[num])  \n",
    "    #Print the label converted back to a number\n",
    "    label = train_labels[num].argmax(axis=0)\n",
    "    #Reshape the 768 values to a 28x28 image\n",
    "    image = train_images[num].reshape([28,28])\n",
    "    plt.title('Sample: %d  Label: %d' % (num, label))\n",
    "    plt.imshow(image, cmap=plt.get_cmap('gray_r'))\n",
    "    plt.show()\n",
    "    \n",
    "display_sample(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's where things get exciting. All that code we wrote in Tensorflow creating placeholders, variables, and defining a bunch of linear algebra for each layer in our neural network? None of that is necessary with Keras!\n",
    "\n",
    "We can set up the same layers like this. The input layer of 784 features feeds into a ReLU layer of 512 nodes, which then goes into 10 nodes with softmax applied. Couldn't be simpler:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(512, activation='relu', input_shape=(784,)))\n",
    "model.add(Dense(10, activation='softmax'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can even get a nice description of the resulting model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense (Dense)                (None, 512)               401920    \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 10)                5130      \n",
      "=================================================================\n",
      "Total params: 407,050\n",
      "Trainable params: 407,050\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting up our optimizer and loss function is just as simple. We will use the RMSProp optimizer here. Other choices include Adagrad, SGD, Adam, Adamax, and Nadam. See https://keras.io/optimizers/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(loss='categorical_crossentropy',\n",
    "              optimizer=RMSprop(),\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training our model is also just one line of code with Keras. Here we'll do 10 epochs with a batch size of 100. Keras is slower, and if we're not running on top of a GPU-accelerated Tensorflow this can take a fair amount of time (that's why I've limited it to just 10 epochs.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/10\n",
      " - 4s - loss: 0.2425 - acc: 0.9288 - val_loss: 0.1244 - val_acc: 0.9612\n",
      "Epoch 2/10\n",
      " - 4s - loss: 0.0972 - acc: 0.9716 - val_loss: 0.0944 - val_acc: 0.9716\n",
      "Epoch 3/10\n",
      " - 3s - loss: 0.0653 - acc: 0.9803 - val_loss: 0.0672 - val_acc: 0.9792\n",
      "Epoch 4/10\n",
      " - 3s - loss: 0.0466 - acc: 0.9857 - val_loss: 0.0726 - val_acc: 0.9771\n",
      "Epoch 5/10\n",
      " - 4s - loss: 0.0352 - acc: 0.9896 - val_loss: 0.0690 - val_acc: 0.9797\n",
      "Epoch 6/10\n",
      " - 4s - loss: 0.0267 - acc: 0.9919 - val_loss: 0.0686 - val_acc: 0.9801\n",
      "Epoch 7/10\n",
      " - 4s - loss: 0.0209 - acc: 0.9939 - val_loss: 0.0727 - val_acc: 0.9795\n",
      "Epoch 8/10\n",
      " - 4s - loss: 0.0164 - acc: 0.9956 - val_loss: 0.0661 - val_acc: 0.9818\n",
      "Epoch 9/10\n",
      " - 4s - loss: 0.0125 - acc: 0.9967 - val_loss: 0.0787 - val_acc: 0.9802\n",
      "Epoch 10/10\n",
      " - 4s - loss: 0.0104 - acc: 0.9971 - val_loss: 0.0699 - val_acc: 0.9832\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(train_images, train_labels,\n",
    "                    batch_size=100,\n",
    "                    epochs=10,\n",
    "                    verbose=2,\n",
    "                    validation_data=(test_images, test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But, even with just 10 epochs, we've outperformed our Tensorflow version considerably!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss: 0.06991298494907751\n",
      "Test accuracy: 0.9832\n"
     ]
    }
   ],
   "source": [
    "score = model.evaluate(test_images, test_labels, verbose=0)\n",
    "print('Test loss:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before let's visualize the ones it got wrong. As this model is much better, we'll have to search deeper to find mistakes to look at."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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I2ATFCwSwf6ObM7PmqTv8kkYBS4ELIyJ9wfeu082Q1COpJ3V9vJm1Vl3hl7QXRfBviogflYM3Sxpb1scCW/qbNiLmR0R3RHR3dXU1omcza4Ca4Zck4DrgiYj4ekXpdqDvY2mnA7c1vj0za5Z63tJ7LHAO8JikR8phFwPzgJslfQJYB5zVnBY7w+zZ1U9m1PqI6HXr1iXrp59+erK+efPmZH0wLrnkkmT905/+dNOWbe1VM/wR8StAVcrpk7xm1rF8hZ9Zphx+s0w5/GaZcvjNMuXwm2XK4TfLlD+6u06DeVttresAVq1aNeB5mw2U1/xmmXL4zTLl8JtlyuE3y5TDb5Yph98sUw6/WaYcfrNMOfxmmXL4zTLl8JtlyuE3y5TDb5Yph98sUw6/WaYcfrNMOfxmmXL4zTLl8JtlyuE3y5TDb5Yph98sUw6/WaZqhl/SQZKWS3pC0uOSZpXD50p6TtIj5depzW/XzBqlnpt27AA+FxEPSdoHWCFpWVn7RkR8rXntmVmz1Ax/RGwCNpWPX5b0BDC+2Y2ZWXPt0T6/pInA0cD95aDPSFopaYGk/apMM0NSj6Se3t7eQTVrZo1Td/gljQKWAhdGxDbgGuBQ4CiKLYMr+5suIuZHRHdEdHd1dTWgZTNrhLrCL2kviuDfFBE/AoiIzRGxMyJeB74LTGlem2bWaPUc7RdwHfBERHy9YvjYitE+DPhWs2ZDSD1H+48FzgEek/RIOexiYJqko4AA1gLnN6VDM2uKeo72/wpQP6U7Gt+OmbWKr/Azy5TDb5Yph98sUw6/WaYcfrNMOfxmmXL4zTLl8JtlyuE3y5TDb5Yph98sUw6/WaYcfrNMOfxmmVJEtG5hUi/wbMWgMcDWljWwZzq1t07tC9zbQDWyt4Mjoq7Py2tp+N+0cKknIrrb1kBCp/bWqX2BexuodvXmzX6zTDn8Zplqd/jnt3n5KZ3aW6f2Be5toNrSW1v3+c2sfdq95jezNnH4zTLVlvBLOlnS/0h6StLsdvRQjaS1kh4rbzve0+ZeFkjaImlVxbDRkpZJWl1+7/ceiW3qrSNu2564rXxbn7tOu919y/f5JQ0HngQ+BGwAHgSmRcSvW9pIFZLWAt0R0fYLQiRNBbYD34+II8phVwAvRMS88oVzv4i4qEN6mwtsb/dt28u7SY2tvK08cCbwj7TxuUv09THa8Ly1Y80/BXgqIp6JiNeAHwBntKGPjhcR9wAv7Db4DGBh+XghxT9Py1XprSNExKaIeKh8/DLQd1v5tj53ib7aoh3hHw+sr/h5A218AvoRwM8lrZA0o93N9OOAiNgExT8TsH+b+9ldzdu2t9Jut5XvmOduILe7b7R2hL+/W3910vnGYyPiGOAU4IJy89bqU9dt21uln9vKd4SB3u6+0doR/g3AQRU/vxPY2IY++hURG8vvW4Bb6bxbj2/uu0Ny+X1Lm/t5Qyfdtr2/28rTAc9dJ93uvh3hfxA4TNK7JL0NOBu4vQ19vImkvcsDMUjaGziRzrv1+O3A9PLxdOC2Nvayi065bXu128rT5ueu025335Yr/MpTGf8ODAcWRMRlLW+iH5IOoVjbQ3EH40Xt7E3SYuB4ird8bgbmAD8GbgYmAOuAsyKi5QfeqvR2PMWm6xu3be/bx25xb38J/BJ4DHi9HHwxxf512567RF/TaMPz5st7zTLlK/zMMuXwm2XK4TfLlMNvlimH3yxTDr9Zphx+s0z9Px3wqAPlPN0EAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hN0uUj/OPcuPGjSusP/jgg4X1U089tZXt7Gbq1KmF9U996lOF9UmTJrWyneR4zW+WKIffLFEOv1miHH6zRDn8Zoly+M0S5fCbJarmcX5Jk4HbgLcDu4AFEfEFSfOAC4H+fNTLI+KBdjVq7XHyyScX1nft2tWhTqzT6vmQzw5gbkQslzQOeFLSQ3nt+oi4tn3tmVm71Ax/RGwANuT3t0paBUxsd2Nm1l7Des8vaQowDViaD7pI0s8k3SJp3yrPmSOpT1Jff3//UKOYWQnqDr+kfYB7gI9HxOvAl4DDgGPJtgyuG+p5EbEgInojorenp6cFLZtZK9QVfkljyIJ/R0TcCxARGyNiZ0TsAm4CprevTTNrtZrhV/b1rzcDqyLi8xXDJ1SMdhbwTOvbM7N2qWdv/4nAecBKSSvyYZcDsyQdCwSwFvhIWzo0s7aoZ2//E8BQX/7uY/pmI5g/4WeWKIffLFEOv1miHH6zRDn8Zoly+M0S5fCbJcrhN0uUw2+WKIffLFEOv1miHH6zRDn8Zoly+M0SpYjo3MykfuCFikHjgc0da2B4urW3bu0L3FujWtnbIRFR1/fldTT8b5q51BcRvaU1UKBbe+vWvsC9Naqs3rzZb5Yoh98sUWWHf0HJ8y/Srb11a1/g3hpVSm+lvuc3s/KUveY3s5I4/GaJKiX8kk6X9Jyk5yVdVkYP1UhaK2mlpBWS+kru5RZJmyQ9UzFsP0kPSfpF/nPIaySW1Ns8SS/ny26FpPeW1NtkST+QtErSzyVdnA8vddkV9FXKcuv4e35JewL/A/wlsA5YBsyKiGc72kgVktYCvRFR+gdCJJ0EbANui4ip+bDPAVsiYn7+wrlvRFzaJb3NA7aVfdn2/GpSEyovKw+cCVxAicuuoK/3U8JyK2PNPx14PiLWRMQbwDeAmSX00fUi4nFgy6DBM4GF+f2FZP88HVelt64QERsiYnl+fyswcFn5UpddQV+lKCP8E4GXKh6vo8QFMIQAlkh6UtKcspsZwoERsQGyfybggJL7GazmZds7adBl5btm2TVyuftWKyP8Q136q5uON54YEccBZwAfyzdvrT51Xba9U4a4rHxXaPRy961WRvjXAZMrHk8C1pfQx5AiYn3+cxOwiO679PjGgSsk5z83ldzP73TTZduHuqw8XbDsuuly92WEfxlwhKRDJe0NfABYXEIfbyJpbL4jBkljgRl036XHFwOz8/uzgftK7GU33XLZ9mqXlafkZddtl7sv5RN++aGMfwX2BG6JiKs63sQQJL2DbG0P2RWM7yyzN0l3AaeQnfK5EbgC+DZwN3Aw8CJwTkR0fMdbld5OIdt0/d1l2wfeY3e4t3cD/wmsBHblgy8ne39d2rIr6GsWJSw3f7zXLFH+hJ9Zohx+s0Q5/GaJcvjNEuXwmyXK4TdLlMNvlqj/A/gZZrs2UtjfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8sB3LzZY0IGlgcHCwkR7NrA3qCr+k0RTB/15E3FRO3ihpXFkfB2wabtmIWBgR/RHR39fX14qezawFaoZfkoArgRUR8bWK0hLg9PL26cCtrW/PzNqlnkt6jwBmAY9JeqScNhdYANwg6RPAU8Ap7WmxN0ybNq1qbeLEicllly1blqzPnTs3WT/zzDOT9dTlxkuWLEkue8cddyTrmzdvTtZrOfXUU6vWal2Sm8Mw2d1UM/wR8WtAVcpTW9uOmXWK3+FnlimH3yxTDr9Zphx+s0w5/GaZcvjNMuWP7q7TTjtVf5ysNdzzmjVrkvVal83WqrfTIYcckqyfffbZyfqsWbOq1moNXW7t5T2/WaYcfrNMOfxmmXL4zTLl8JtlyuE3y5TDb5Ypn+dvgUWLFiXrRx55ZLJe65r7u+66K1k/66yzqtZOPvnk5LLjxo1L1seOHZus77HHHsm69S7v+c0y5fCbZcrhN8uUw2+WKYffLFMOv1mmHH6zTPk8fwsU45pUN3v27KbqZu3gPb9Zphx+s0w5/GaZcvjNMuXwm2XK4TfLlMNvlqma4Ze0v6R7JK2QtFzSZ8vp8yWtl/RI+VV9AHsz6zn1vMlnC3BuRCyVtDvwkKShT5f4ekR8pX3tmVm71Ax/RGwANpS3X5S0Ati33Y2ZWXtt12t+SZOAdwO/KSd9RtKjkq6StFeVZWZLGpA0MDg42FSzZtY6dYdf0m7AjcA5EfEC8C3gAOAwimcGXx1uuYhYGBH9EdHf19fXgpbNrBXqCr+k0RTB/15E3AQQERsjYmtEvApcAUxpX5tm1mr1HO0XcCWwIiK+VjG98mNfPwwsa317ZtYu9RztPwKYBTwm6ZFy2lxgpqTDgABWA59qS4dm1hb1HO3/NTDcBeu3tb4dM+sUv8PPLFMOv1mmHH6zTDn8Zply+M0y5fCbZcrhN8uUw2+WKYffLFMOv1mmHH6zTDn8Zply+M0y5fCbZUoR0bmNSYPAmopJY4BnO9bA9unV3nq1L3BvjWplbxMjoq7Py+to+N+wcWkgIvq71kBCr/bWq32Be2tUt3rz036zTDn8ZpnqdvgXdnn7Kb3aW6/2Be6tUV3prauv+c2se7q95zezLnH4zTLVlfBLOl7Sf0taJen8bvRQjaTVkh4rhx0f6HIvV0naJGlZxbS9Jd0l6Yny+7BjJHapt54Ytj0xrHxX77teG+6+46/5Je0MPA78PbAOeBCYGRG/62gjVUhaDfRHRNffECLp/cBLwLURcXA57cvAcxGxoHzg3CsizuuR3uYDL3V72PZyNKlxlcPKAycBZ9DF+y7R10fpwv3WjT3/FGBVRDwZEX8Gvg9M70IfPS8i7gOe22bydGBReXsRxT9Px1XprSdExIaIWFrefhEYGla+q/ddoq+u6Eb49wXWVvy8ji7eAcMI4E5JD0ma3e1mhjE2IjZA8c8EvLXL/Wyr5rDtnbTNsPI9c981Mtx9q3Uj/MMN/dVL5xuPiIjDgROAOeXTW6tPXcO2d8oww8r3hEaHu2+1boR/HbB/xc/7AU93oY9hRcTT5fdNwM303tDjG4dGSC6/b+pyP6/ppWHbhxtWnh6473ppuPtuhP9BYLKkt0l6E/AxYEkX+ngDSW8uD8Qg6c3AsfTe0ONLgNPL26cDt3axl9fplWHbqw0rT5fvu14b7r4r7/ArT2VcBuwMXBURl3S8iWFIejvF3h6KEYyv72ZvkhYDR1Nc8rkRmAfcAtwATACeAk6JiI4feKvS29EUT11fG7Z96DV2h3s7EvgV8Bjwajl5LsXr667dd4m+ZtKF+81v7zXLlN/hZ5Yph98sUw6/WaYcfrNMOfxmmXL4zTLl8Jtl6v8BqoO1QzC0yZwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for x in range(1000):\n",
    "    test_image = test_images[x,:].reshape(1,784)\n",
    "    predicted_cat = model.predict(test_image).argmax()\n",
    "    label = test_labels[x].argmax()\n",
    "    if (predicted_cat != label):\n",
    "        plt.title('Prediction: %d Label: %d' % (predicted_cat, label))\n",
    "        plt.imshow(test_image.reshape([28,28]), cmap=plt.get_cmap('gray_r'))\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "You can see most of the ones it's having trouble with, are images a human would have trouble with as well!\n",
    "\n",
    "## Excercise\n",
    "\n",
    "As before, see if you can improve on the results! Does running more epochs help considerably? How about trying different optimizers?\n",
    "\n",
    "You can also take advantage of Keras's ease of use to try different topologies quickly. Keras includes a MNIST example, where they add an additional layer, and use Dropout at each step to prevent overfitting, like this:\n",
    "\n",
    "`\n",
    "model = Sequential()\n",
    "model.add(Dense(512, activation='relu', input_shape=(784,)))\n",
    "model.add(Dropout(0.2))\n",
    "model.add(Dense(512, activation='relu'))\n",
    "model.add(Dropout(0.2))\n",
    "model.add(Dense(10, activation='softmax'))\n",
    "`\n",
    "\n",
    "Try adapting that to our code above and see if it makes a difference or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
